It is almost impossible to describe the acceleration in the Tesla Model S electric car. It would be brutal except there is almost no noise, the leather-lined cabin is pampering and calm, and the ride over bumps so gentle and smooth.

But it accelerates so fast it challenges the senses. The closest example I can think of is the start of a high-speed roller coaster.

Explore the 2014 Tesla Model S Range

Your head hits the headrest behind you, your eyes push back into their sockets and you hang on.

The difference is that the Tesla isn't on rails, you can steer it wherever you want to go. Well, almost.

The maximum range in ideal driving conditions is 500km, and it requires a unique charging adaptor (to handle 40 amps), so you can't top up at home or work without a $1000 installation. Floor it like we did and maximum range suddenly drops to 160km.

Which means, for now, it's one of the most amazing cars money can buy providing you don't venture further than between 80km and 250km from home, because otherwise you'd have to tow it back.

Anyone who dismisses electric cars as the weaklings of the automotive industry need to go for a ride in one of these. Without exaggeration, it would give a supercharged HSV GTS – Australia's fastest and most powerful sedan – a bloody nose before it overtook a Mercedes-Benz AMG E63. And you wouldn't even hear it coming.

We couldn't replicate Tesla's claim of a 0 to 100km/h time of 3.8 seconds, but it'll repeatedly complete the feat in a sub 5.0-second time with the same effort as brushing your teeth.

Then there is the surprise and delight factor: it has the largest display screen of any car on sale. Forget tablet, it's more like a desk-top screen that has been fitted vertically.

There are only two buttons inside: the glovebox and hazard light switch. The doors open as you approach the car, and lock as you drive off, blending in with the profile of the doors, so no-one could car-jack you if they tried.

Some of the technology is genius, such as the memory setting for raising the suspension for steep drive-ways. When you slow down for the same drive-way next time, the car remembers the GPS position and does it automatically.

The car turns itself off after you walk away, which is an eerie feeling and took some getting used to.

It's the one electric car that looks like it's actually worth the price being asked. The Tesla Model S easily competes with other cars in the $100,000 to $220,000 price bracket (the price depends on the size of the battery pack and the number of options).

But it's worth noting a car with all this technology is able to limbo to this price because a large chunk of it has been subsidised by a US government trying to reduce its dependence on oil. So the Tesla Model S is not exactly competing on a level playing field just yet.